# Find the Middle Term in the Expansion Of: (I) ( 2 3 X − 3 2 X ) 20 - Mathematics

Find the middle term in the expansion of:

(i)  $\left( \frac{2}{3}x - \frac{3}{2x} \right)^{20}$

#### Solution

(i) Here,
n = 20  (Even number)
Therefore, the middle term is the $\left( \frac{n}{2} + 1 \right)$ th term, i.e., the 11th term.

$Now,$
$T_{11} = T_{10 + 1}$
$= ^{20}{}{C}_{10} \left( \frac{2}{3}x \right)^{20 - 10} \left( \frac{3}{2x} \right)^{10}$
$= ^{20}{}{C}_{10} \frac{2^{10}}{3^{10}} \times \frac{3^{10}}{2^{10}} x^{10 - 10}$
$=^{20}{}{C}_{10}$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 18 Binomial Theorem
Exercise 18.2 | Q 13.1 | Page 38